A rectangular tank has a length of 10 m, a width of 3 m, and a height of 4 m, as shown - Junior Cycle Mathematics - Question 9 - 2014

To find the total surface area, we use the formula:

$SA = 2(lh + lw + hw)$ Where:

• $l$ = length = 10 m
• $w$ = width = 3 m
• $h$ = height = 4 m

Substituting the values:

$SA = 2((10 \times 4) + (10 \times 3) + (3 \times 4))$ $SA = 2(40 + 30 + 12)$ $SA = 2(82) = 164 \text{ m}^2$

The volume of the tank can be calculated using the formula:

$V = l \times w \times h$

Substituting the dimensions:

$V = 10 \times 3 \times 4 = 120 \text{ m}^3$

To convert this into litres, we use the conversion factor:

$V = 120 \text{ m}^3 \times 1000 = 120000 \text{ litres}$

The tank is filled to a depth of 50 cm, which is equivalent to 0.5 m. The volume of water is calculated using the base area multiplied by the height of the water:

$V_{water} = l \times w \times h_{water}$

Substituting the values:

$V_{water} = 10 \times 3 \times 0.5 = 15 \text{ m}^3$

To convert to litres:

$V_{water} = 15 \text{ m}^3 \times 1000 = 15000 \text{ litres}$